Processes for production of thermoinsulating mats or felts of mineral fibers (glass fibers or rock fibers) whose orientation is almost random, as described in European patent 0 133 083, are already known. These products have advantageous qualities, but they have a high density (from 50 to 150 kg/m3) and do not have a sufficient flexibility for some applications, in particular for applying such insulating mats to cylindrical surfaces, e.g., of tanks, without forming pockets of condensation on the side in contact with the cylindrical surface and without forming cracks in their outside surface.